1. Field of Invention
The present invention relates to a method of fast image reconstruction, wherein an interpolation with variable interpolation intervals and an interpolation with variable interpolation intervals where windowing is carried out by means of any available window functions, which are novel and applicable to instruments which need interpolation such as Fourier domain Optical Coherent Tomography (OCT), are adopted, in order to achieve fast image reconstruction.
2. Description of Prior Art
In the field of fast image reconstruction, as a novel contactless optical detection system with high resolution, a Fourier domain Optical Coherent Tomography (OCT) system obtains structure information, Doppler information and polarization information of an object through scanning the object longitudinally by means of optical interference and then though 2-D or 3-D reconstruction. Therefore, such system can find its application in a variety of fields including medical imaging and industrial damage detection. According to the Fourier domain OCT technology, a reference light and a signal light interferes with each other in an optical splitter 3, and then the interference signal undergoes spectrum-division at a diffraction grating 9 and then is focused by a lens 10 onto a linear scanning CCD 11, which converts the analog signal into a digital signal, as shown in FIG. 2. A spectrometer 8 consists of the diffraction grating 9, the lens 10 and the linear scanning CCD 11. Wavelengths collected by the CCD 11, which exit from the grating, are in a linear distribution. However, data reconstruction requires a linear distribution in a K space of the wavelength information, and thus needs interpolation of data. For a Fourier domain OCT system, various types of interpolations are applicable to fast image reconstruction, for example, discrete Fourier transform with zero-padding interpolation, B-spline fitting, direct linear interpolation or the like. However, most Fourier domain OCT systems adopt a combination of the discrete Fourier transform with zero-padding interpolation and the direct linear interpolation. Specifically, N points of data are subject to a discrete Fourier transform to obtain N points of data in a frequency domain, which then are padded with M*N points of zero values at high-frequency points to obtain M*N+N points of data in the frequency domain, which then are subject to an inverse Fourier transform to obtain M*N+N points of data. Here, M is a factor of zero-padding. Finally, N points of interpolated data are obtained by means of linear interpolation. Suppose a vector of data collected by a Fourier domain OCT system through scanning is {right arrow over (x)}={x1, x2, . . . , xN}, then the conventional discrete Fourier transform with zero-padding interpolation comprises steps of:
1) carrying out discrete Fourier transform on the data to obtain a new set of data:
                    X        1            ⁡              (        i        )              =                  ∑                  n          =          0                          N          -          1                    ⁢                        x                      n            +            1                          ⁢                  exp          ⁡                      (                                          -                j                            ⁢                                                2                  ⁢                                                                          ⁢                  π                                N                            ⁢              in                        )                                ;2) carrying out zero-padding interpolation on the new set of data to obtain a set of data padded with zeros at a factor of M:
            X      2        ⁡          (      i      )        =      {                                                                      X                1                            ⁡                              (                i                )                                      ,                                                0            ≤            i            ≤                                          N                2                            -              1                                                                        0            ,                                    otherwise                                                                                X                1                            ⁡                              (                                  i                  -                  MN                                )                                      ,                                                                                                                    (                                          M                      +                      1                                        )                                    *                  N                                -                                  N                  2                                            ≤              i              ≤                                                                    (                                          M                      +                      1                                        )                                    *                  N                                -                1                                      ;                              3) carrying out inverse Fourier transform on the set of data padded with zeroes at the factor M to obtain a set of data which are expanded at a factor of (M+1); and4) carrying out linear interpolation on the expanded data in accordance with a linear distribution in the K space to obtain interpolated data.
Though such method is simple and well-developed, it has disadvantages such as significant amount of computations, as a result of which requirements of real-time image reconstruction cannot be satisfied, and fixed interpolation intervals and interpolation precision determined by the factor M of zero-padding, as a result of which interpolation intervals cannot be varied as desired. Further, the interpolation precision is degraded due to discrete Fourier transform with zero-padding interpolation followed by linear interpolation. All those limitations strictly restrict the fast image reconstruction application of Fourier domain OCT systems.